A digital communication system uses error correction codes when correcting errors in data which occur due to, for example, influence of noise received in a communication path.
The error correction codes are implemented by error correction encoding at the transmitter side and error correction decoding at the receiver side. The error correction decoding can be broadly classified into two types: one is called as hard decision decoding and the other is called as soft decision decoding.
Digital data transmitted in the digital communication system is composed of bit information of “0” or “1”. When performing hard decision decoding., a binary decision is made to decide that a value of each bit of digital data is “0” or “1” by comparing the value of each bit with as threshold value. The hard decision decoding of the digital data is performed by using hard decision values which are the results of the decision.
On the other hand, when performing, soft decision decoding, instead of performing a binary decision of “0” or “1”, soft decision values indicating the probability of “0” or “1”, likelihood, or log-likelihood ratio (LLR) are calculated. The soft decision decoding of the digital data is performed by using the soft decision values.
The soft decision decoding has a strong error correction capability compared to the hard decision decoding. For codes to be used together with soft decision decoding, there are turbo codes and LDPC (Low-Density Parity-Check) codes.
Soft decision values are generated, from a received symbol being received data, depending on a digital modulation scheme of a transmission symbol being transmission data.
When the digital modulation scheme used in the digital communication system is a multilevel modulation scheme, e.g., PSK (Phase Shift Keying), APSK (Amplitude Phase Shift Keying), or QAM (Quadrature amplitude modulation), one transmission symbol is composed of a plurality of bits.
Assuming that an LLR being a log-likelihood ratio of a k-th bit of a transmission symbol is “Lk”, this Lk can be calculated by the following equation (1):
                              L          k                -                  ln          ⁢                                    ∑                                                s                  i                                ∈                                  C                                      k                    ,                    0                                                                        ⁢                                                  ⁢                          exp              ⁡                              (                                  -                                                                                                                                      r                          -                                                      s                            i                                                                                                                      2                                                              2                      ⁢                                              σ                        2                                                                                            )                                                    -                  ln          ⁢                                    ∑                                                s                  i                                ∈                                  C                                      k                    ,                    1                                                                        ⁢                                                  ⁢                          exp              ⁡                              (                                  -                                                                                                                                      r                          -                                                      s                            i                                                                                                                      2                                                              2                      ⁢                                              σ                        2                                                                                            )                                                                        (        1        )            
In the equation (1), “r” denotes the position vector (I coordinate and Q coordinate) of a received symbol (a received signal point), “si” denotes the position vector of the transmission symbol (a transmission signal point), “Ck,0” denotes a set of all transmission symbol points each of whose k-th bit is “0”, “Ck,1” denotes a set of all transmission symbol points each of whose k-th bit is “1”, and “σ” denotes the standard deviation of Gaussian noise in a communication path.
Calculation of an LLR by the equation (1) requires to compute a plurality of exponential functions “exp” before adding, up computation results of the exponential functions “exp”, and to further compute a logarithmic function “In” for the result of the addition. Accordingly, the amount of computation may become enormous.
Therefore, it is not realistic to implement the computation of an LLR by the equation (1) by a circuit, in terms of circuit size.
The following Non-Patent Literature 1 discloses an LLR approximate computation technique in which only a maximum value among the computation results of the exponential functions “exp” in the equation (1) is used while other values of the computation results are ignored.
The following equation (2) is a calculation expression for “Lk” by the above-described approximate computation technique:
                                                                        L                k                            =                            ⁢                                                n                  ⁢                                                            ∑                                                                        s                          i                                                ∈                                                  C                                                      k                            ,                            0                                                                                                                ⁢                                                                                  ⁢                                          exp                      ⁡                                              (                                                  -                                                                                                                                                                                      r                                  -                                                                      s                                    i                                                                                                                                                              2                                                                                      2                              ⁢                                                              σ                                2                                                                                                                                    )                                                                                            -                                  ln                  ⁢                                                            ∑                                                                        s                          i                                                ∈                                                  C                                                      k                            ,                            1                                                                                                                ⁢                                                                                  ⁢                                          exp                      ⁡                                              (                                                  -                                                                                                                                                                                      r                                  -                                                                      s                                    i                                                                                                                                                              2                                                                                      2                              ⁢                                                              σ                                2                                                                                                                                    )                                                                                                                                                                    ≈                            ⁢                                                ln                  ⁢                                                                          ⁢                                                            max                                                                        s                          j                                                ∈                                                  C                                                      k                            ,                            0                                                                                                                ⁢                                          exp                      ⁡                                              (                                                  -                                                                                                                                                                                      r                                  -                                                                      s                                    i                                                                                                                                                              2                                                                                      2                              ⁢                                                              σ                                2                                                                                                                                    )                                                                                            -                                  ln                  ⁢                                                                          ⁢                                                            max                                                                        s                          i                                                ∈                                                  C                                                      k                            ,                            1                                                                                                                ⁢                                          exp                      ⁡                                              (                                                  -                                                                                                                                                                                      r                                  -                                                                      s                                    i                                                                                                                                                              2                                                                                      2                              ⁢                                                              σ                                2                                                                                                                                    )                                                                                                                                                                    =                            ⁢                                                                                          -                                                                                                                              r                            -                                                          s                                                              k                                ,                                0                                ,                                min                                                                                                                                                              2                                                              +                                                                                                                    r                          -                                                      s                                                          k                              ,                              1                              ,                              min                                                                                                                                                  2                                                                            2                    ⁢                                          σ                      2                                                                      :=                                  L                                      1                    ,                    k                                                                                                          (        2        )            
In equation (2), “Sk,0,min” denotes the position vector of a transmission symbol point that is closest to the received signal point “r” among the transmission symbol points each of whose k-th bit is “0”, and “Sk,1,min” denotes the position vector of a transmission symbol point that is closest to the received signal point “r” among the transmission symbol points each of whose k-th bit is “1”.
In addition, the following Patent Literature I discloses a method of efficiently calculating LLRs by using symmetry of mapping in gray-mapped QAM based on the LLR approximate computation technique disclosed in the Non-Patent Literature 1.
However, the method disclosed in Patent Literature 1 is a method only applicable to gray-mapped ones, and there is no known gray-mapping with excellent characteristics for QAM having an odd power of 2 number of modulation levels such as 32QAM and 128QAM.
In general, in QAM whose number of modulation levels is an even power of 2 and which is known for its gray mapping with excellent characteristics, the LLR of each bit depends on only an I-ch (in-phase component) coordinate or a Q-ch (quadrature component) coordinate. Therefore, LLRs with high approximation accuracy can be calculated with a relatively small amount of computation.
On the other hand, in QAM or APSK, etc., whose numbers of modulation levels are an odd power of 2, the LLR of each bit depends on both of the I-ch coordinate and the Q-ch coordinate. Therefore, calculation of LLRs with high approximation accuracy requires a large amount of computation.
Meanwhile, when a modulation symbol is differentially encoded, modulation schemes, such as differential encoding QPSK or differential encoding QAM, may be used.
In these modulation schemes, demodulation is possible by a receiver performing differential detection, and in general, coherent detection is not required. Note, however, that by the receiver performing coherent detection, higher reception performance than that exerted when differential detection is performed can be exerted.
In a modulation scheme where a modulation symbol is differentially encoded, assuming that the LLR of a differentially encoded k-th bit is “Lk”, this Lk can be calculated by the following equation (3):
                              L          k                =                              ln            ⁢                                          ∑                                                      (                                                                  q                        i                                            ,                                              q                        j                                                              )                                    ∈                                      D                                          k                      ,                      0                                                                                  ⁢                                                          ⁢                              [                                                      1                                          2                      ⁢                                              πσ                        2                                                                              ⁢                                      exp                    ⁡                                          (                                              -                                                                                                                                                                                                            r                                  1                                                                -                                                                  q                                  i                                                                                                                                                    2                                                                                2                            ⁢                                                          σ                              2                                                                                                                          )                                                        ⁢                                      exp                    ⁡                                          (                                              -                                                                                                                                                                                                            r                                  2                                                                -                                                                  q                                  j                                                                                                                                                    2                                                                                2                            ⁢                                                          σ                              2                                                                                                                          )                                                                      ]                                              -                      ln            ⁢                                          ∑                                                      (                                                                  q                        i                                            ,                                              q                        j                                                              )                                    ∈                                      D                                          k                      ,                      1                                                                                  ⁢                                                          ⁢                              [                                                      1                                          2                      ⁢                                              πσ                        2                                                                              ⁢                                      exp                    ⁡                                          (                                              -                                                                                                                                                                                                            r                                  1                                                                -                                                                  q                                  i                                                                                                                                                    2                                                                                2                            ⁢                                                          σ                              2                                                                                                                          )                                                        ⁢                                      exp                    ⁡                                          (                                              -                                                                                                                                                                                                            r                                  2                                                                -                                                                  q                                  j                                                                                                                                                    2                                                                                2                            ⁢                                                          σ                              2                                                                                                                          )                                                                      ]                                                                        (        3        )            
In equation (3), “r1” denotes the position vector of a reference symbol (i.e., a received symbol which has been received one time previous to the present time), “r2” denotes the position vector of the received symbol at the present time, and “Dk,1” denotes a set of pairs of transmission symbols (qi, qi) (i.e., pairs of a reference symbol at the time of transmission and a received symbol at the present time) each of whose k-th bit before differential encoding is “1” (1+0, 1).
In addition, the following Patent Literature 2 discloses a method of efficiently calculating LLRs when a modulation scheme is differential encoding QPSK.
However, a method of calculating LLRs for differential encoding multilevel modulation is not disclosed.
Patent Literature 1: JP 2002-330188 A
Patent Literature 2: WO 2012/070369 A
Non-Patent Literature 1 : F. Tosato and P. Bisaglia, “Simplified soft-output demapper for binary interleaved COFDM with application to HIPERLAN/2,” in Proc. Int, Conf. Commun., Sep. 2002, pp. 664-668.